Model Checking Software

Volume 3925 of the series Lecture Notes in Computer Science pp 71-88

Don’t Know in Probabilistic Systems

  • Harald FecherAffiliated withInstitute of Informatics, University of Kiel
  • , Martin LeuckerAffiliated withInstitute of Informatics
  • , Verena WolfAffiliated withInstitute of Informatics, University of Mannheim

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In this paper the abstraction-refinement paradigm based on 3-valued logics is extended to the setting of probabilistic systems. We define a notion of abstraction for Markov chains. To be able to relate the behavior of abstract and concrete systems, we equip the notion of abstraction with the concept of simulation. Furthermore, we present model checking for abstract probabilistic systems (abstract Markov chains) with respect to specifications in probabilistic temporal logics, interpreted over a 3-valued domain. More specifically, we introduce a 3-valued version of probabilistic computation-tree logic (PCTL) and give a model checking algorithm w.r.t. abstract Markov chains.